Connectedness of approximate solutions set for vector equilibrium problems in Hausdorff topological vector spaces. (English) Zbl 1315.47055
Summary: In this paper, a scalarization result of \(\varepsilon\)-weak efficient solution for a vector equilibrium problem (VEP) is given. Using this scalarization result, the connectedness of \(\varepsilon\)-weak efficient and \(\varepsilon\)-efficient solutions sets for the VEPs are proved under some suitable conditions in real Hausdorff topological vector spaces. The main results presented in this paper improve and generalize some known results in the literature.
MSC:
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
Keywords:
vector equilibrium problem; scalarization method; \(\varepsilon\)-weak efficient solution; \(\varepsilon\)-efficient solution; connectednessReferences:
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